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We demonstrate that the concept of Goldstone bosons can be exploited for phonon control and thermal conductivity reduction of materials. By studying lattice dynamics of the Sn filled skutterudite SnFe₄Sb₁₂, we find Sn off-centers in its coordination cage in contrast to common rare earth fillers. This leads to low-frequency optical phonons even below 1 THz associated mainly with Sn motions, but with strong collective motion of other atoms in the host skutterudite lattice. The optical modes transverse to the Sn off-centering direction are identified as Goldstone type modes in association with a three-dimensional Mexican hat-like potential energy surface. The interaction of these collective Goldstone modes with the host heat-carrying phonons leads to ultralow thermal conductivities. This provides a novel mechanism to reduce thermal conductivity by exploiting the complex physics of the lattice dynamics of solids.